Question

i'm having a bit of trouble with U substitution like how do I do it exactly with a problem like X/1+X^4 dx

Answer 1

Do you mean
\[\int\frac{x}{1+x^4}dx?\]

Answer 2

yes

Answer 3

Then an ordinary algebraic substitution won't work here. Just a sec, let me try to work this out.

Answer 4

okay then

Answer 5

Alright, I think I have it. Make the following substitution:
\[x=\sqrt{u}, \text{ so}\\
x^2=u, \text{ and}\\
x^4=u^2\]
So, you have
\[dx=\frac{1}{2\sqrt{u}}du\]
Now the integral becomes
\[\int\frac{\sqrt{u}}{1+u^2}\left(\frac{1}{2\sqrt{u}}du\right)\\
\frac{1}{2}\int\frac{1}{1+u^2}du\]
Can you work with that one?

Answer 6

i think so let me give it a try

Answer 7

I have one question where did u get the 1/2\[1\2\sqrt{U}\]

Answer 8

That's from the derivative of sqrt(u):
\[\frac{d}{du}\sqrt{u}=\frac{d}{du}u^{\frac{1}{2}}=\frac{1}{2}u^{-\frac{1}{2}}=\frac{1}{2u^{\frac{1}{2}}}=\frac{1}{2\sqrt{u}}\]

Answer 9

that makes it easier to see